456508228800 has 672 divisors, whose sum is σ = 1642075456000. Its totient is φ = 110361968640.

The previous prime is 456508228783. The next prime is 456508228817. The reversal of 456508228800 is 8822805654.

It is a happy number.

It is an interprime number because it is at equal distance from previous prime (456508228783) and next prime (456508228817).

It is a super-2 number, since 2×456508228800² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (48).

It is a self number, because there is not a number n which added to its sum of digits gives 456508228800.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1204507011 + ... + 1204507389.

Almost surely, 2^456508228800 is an apocalyptic number.

456508228800 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 456508228800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (821037728000).

456508228800 is an abundant number, since it is smaller than the sum of its proper divisors (1185567227200).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

456508228800 is a wasteful number, since it uses less digits than its factorization.

456508228800 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 713 (or 698 counting only the distinct ones).

The product of its (nonzero) digits is 1228800, while the sum is 48.

The spelling of 456508228800 in words is "four hundred fifty-six billion, five hundred eight million, two hundred twenty-eight thousand, eight hundred".